Chapter 4: Unit roots, non-linearities and structural breaks
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It is widely accepted that many time series in economics and finance exhibit trending behaviour in the level (or mean) of the series. Typical examples include asset prices, exchange rates, real GDP, real wage series and so forth. In a recent paper White and Granger (2011) reflect on the nature of trends and make a variety of observations that seem to characterize these. Interestingly, as also noted by Phillips (2005), even though no one understands trends everybody still sees them in the data. In economics and other disciplines, almost all observed trends involve stochastic behaviour and purely deterministic trends are rare. However, a combination of stochastic and deterministic elements including structural changes seems to be a model class which is likely to describe the data well. Potentially the series may contain non-linear features and even the apparent deterministic parts like level and trend may be driven by an underlying stochastic process that determines the timing and the size of breaks. In recent years there has been a focus on stochastic trend models caused by the presence of unit roots. A stochastic trend is driven by a cumulation of historical shocks to the process and hence each shock will have a persistent effect. This feature does not necessarily characterize other types of trends where the source of the trend can be different and some or all shocks may only have a temporary effect.

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